Related papers: Maximum entropy low-rank matrix recovery
Current end-to-end (E2E) and plug-and-play (PnP) image reconstruction algorithms approximate the maximum a posteriori (MAP) estimate but cannot offer sampling from the posterior distribution, like diffusion models. By contrast, it is…
In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless…
Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…
In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with $\ell_1$-loss, where the goal is to recover a low-rank matrix from a limited number of…
We present novel techniques for analyzing the problem of low-rank matrix recovery. The methods are both considerably simpler and more general than previous approaches. It is shown that an unknown (n x n) matrix of rank r can be efficiently…
The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore,…
The reconstruction of images from a small number of projections using the maximum-entropy method (MEM) with the Shannon entropy is considered. MEM provides higher-quality image reconstruction for sources with extended components than the…
The application of the context-adaptive entropy model significantly improves the rate-distortion (R-D) performance, in which hyperpriors and autoregressive models are jointly utilized to effectively capture the spatial redundancy of the…
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…
The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision…
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a…
We investigate the dependence of the maximum entropy method (MEM) reconstruction performance on the default model. The maximum entropy method is a reconstruction technique that utilizes prior information, referred to as the default model,…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve…
In this age of information, images are a critical medium for storing and transmitting information. With the rapid growth of image data amount, visual compression and visual data perception are two important research topics attracting a lot…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…
Large-scale pre-trained language models (LLMs) have demonstrated exceptional performance in various natural language processing (NLP) tasks. However, the massive size of these models poses huge challenges for their deployment in real-world…
Data acquisition efficiency is a central challenge in deploying reinforcement learning in business and healthcare operations, where interactions are costly, slow, and often involve humans in the loop. This paper develops a unified large…